Ok.. have to clear one thing up first. You will have a YOU session first; here they will give you an apptitude test, then there is a little tiny interview, but thats more getting to know you and your motivations for applying to the ADF. Also, there is a quick color-perception test with a nurse, and thats about it.
Following this, you have an Assessment Day, this is what I think you're getting at with your questions.
For a RAN Assessment Day Interview, you would need to identify different types of ships, the present Chief of the Navy, the present Chief of the ADF, the present Defence Minister, where your military training is and what it entails, where you're employment training is and what it entails, the role of your job and your own motivations, strengths and weaknesses. You will be given a good guide of what you need to know.
Hmm.. I never found there Psych interview embarassing. It just seeks to identify your level of maturity and to ensure that you are joining, or seeking to join, for the right reasons. It will ask about the stability in your life, your friends, family, your support circle.. but nothing I found embarassing off memory. How to respond? Honestly.
If anything, the medical would give more reason to be embarassed. If a male, you will be given the "drop your strides.. now cough" treatment. You will also do things like duck-walk and certain types of physical activities in your underwear. As a female, its not quiet so invasive - the DFR will not require you to remove your underwear. However, you will still do the duck-walking etc. in your underwear.
After that, if you are looking at Officer entry you will go before an Officer Selection Board. As a part of a 'gentlemans-agreement' entered to upon going before the OSB, I will not go into detail. However, it will require you to prove your competitiveness for spots.